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   <title>unadjoint :: Functions (Quaternion Toolbox Function Reference)
</title><link rel="stylesheet" href="qtfmstyle.css" type="text/css"></head><body><h1>Quaternion Function Reference</h1><h2>unadjoint</h2>
<p>Unadjoint of a quaternion matrix</p>
<h2>Syntax</h2><p><tt>C = unadjoint(A, F)</tt></p>
<h2>Description</h2>
<p>
This function reverses the result of the <tt>adjoint</tt> function,
so that <tt>unadjoint(adjoint(A)) == A</tt>.
</p>
<p>
<tt>unadjoint(A)</tt> or
<tt>unadjoint(A, 'complex')</tt> assumes <tt>A</tt> is a complex adjoint matrix.
<tt>unadjoint(A, 'real')</tt>    assumes <tt>A</tt> is a real    adjoint matrix.
<tt>unadjoint(A, 'quaternion')</tt> assumes <tt>A</tt> is a quaternion adjoint matrix
(only valid for the case where the original matrix was a complex quaternion
or biquaternion matrix).
The default assumption is a complex adjoint.
</p>

<h2>Examples</h2>
<pre>
&gt;&gt; A = randq(2)
 
A = 2x2 quaternion array
 
&gt;&gt; B = unadjoint(adjoint(A))
 
B = 2x2 quaternion array
 
&gt;&gt; show(A - B)
 
S =
 
     0     0
     0     0

X =
 
     0     0
     0     0

Y =
 
     0     0
     0     0

Z =
 
     0     0
     0     0
</pre>

<h2>See Also</h2>QTFM function: <a href="adjoint.html">adjoint</a><br>
<h2>References</h2><ol><li>F. Z. Zhang, Quaternions and Matrices of Quaternions,
<i>Linear Algebra and its Applications</i>, <b>251</b>,
January 1997, 21-57.


DOI: <a href="http://dx.doi.org/10.1016/0024-3795%2895%2900543-9">10.1016/0024-3795%2895%2900543-9</a></li><li>B. P. Ickes, A New Method for Performing Digital Control System
Attitude Computations using Quaternions, <i>AIAA Journal</i>,
<b>8</b>(1), January 1970, pp13-17, American Institute of Aeronautics
and Astronautics.</li><li>Ward, J. P., Quaternions and Cayley numbers, Kluwer, 1997.</li><li>Todd A. Ell, On Systems of Linear Quaternion Functions, February
2007, arXiv:math/0702084v1, <a href="http://www.arxiv.org/abs/math/0702084">http://www.arxiv.org/abs/math/0702084</a>.
</li><li>Nicolas Le Bihan, Sebastian Miron and Jerome Mars,
MUSIC Algorithm for Vector-Sensors Array using Biquaternions,
<i>IEEE Transactions on Signal Processing</i>,
<b>55</b>(9), September 2007, 4523-4533.

DOI: <a href="http://dx.doi.org/10.1109/TSP.2007.896067">10.1109/TSP.2007.896067</a>.</li></ol>
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